Decomposing temporal changes of biodiversity to loss, survival, and recruitment of individuals: analysis of the North-American avifauna

.title[
# Decomposing temporal changes of biodiversity to loss, survival, and recruitment of individuals: analysis of the North-American avifauna
]
.author[
### <br><br><br><br>François Leroy<br>Marta Jarzyna<br>Petr Keil
]
.institute[
### <br><br><br><br><br>Czech University of Life Sciences<br>Prague
]

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# Temporal change of biodiversity

* Multi-faceted phenomenon (species richness, turnover, abundance)

* Changes through time

* Perturbed by human activities

* sensitive indicator of biodiversity state

* average decline of relative abundance `$\rightarrow$` 69% (*acc.* Living Planet Index)

.center[
`$\Rightarrow$` Marine Sharks and Rays: -71%<br><br>
`$\Rightarrow$` Freshwater: -83%<br><br>
`$\Rightarrow$` -3 billion North-American birds since 70's
]

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# Decomposing abundance change

* Temporal change of abundance ( `$\Delta N$` ) results of `$3$` processes

<br>

<br>
`$$\Rightarrow \Delta N = N_{t1} - N_{t0} = R - L$$`
<br>

`$$\Rightarrow \Delta^2N = \Delta R - \Delta L$$`

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# Decomposing growth rate

* Growth rate: per individual average change

<br>

`$$\Rightarrow \frac{\Delta N}{N_{t0}} = \frac{R}{N_{t0}} - \frac{L}{N_{t0}}$$`

* Recruitment rate `$= \frac{R}{N_{t0}}$`

* Recruitment rate = individual probability of producing an individual

]

* Loss rate `$= \frac{L}{N_{t0}}$`

* Loss rate = individual probability of dying/emigrating

]

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## Problem

`$\Rightarrow$` Assessing the ongoing decrease of abundance does not tell us how loss and recruitment change through time

`$\Rightarrow$` Decrease in recruitment `$\neq$` Increase in loss, but they both result in an acceleration of the decrease of abundance

### From a conservation perspective

`$\rightarrow$` measures to "bend the curve" of recruitment (*e.g.* working on reproductive sucess, protecting breeding habitat)

`$$\neq$$`

`$\rightarrow$` measures to "bend the curve" of loss (*e.g.* reduction of threats, increasing habitat quality)

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## For North-American avifauna, we assessed:

###  1) temporal change of abundance, recruitment and loss from 1987 and 2021

### 2) temporal change of growth rate, recruitment rate and loss rate

### 3) which process (recruitment or loss) is driving temporal change of biodiversity

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# Data - Breeding Bird Survey (BBS)

* Structured data on North American avifauna

* From 1987 to 2021

]

* More than 1000 routes

* 564 species

]

]

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# Model - Dail & Madsen

<br>

`$$N_{t+1} = Survival_{t+1} + Recruitment_{t+1}$$`
.center[

#### with

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`$$Survival_{t+1} \sim Bin(N_t, \omega)$$`

`$$Recruitment_{t+1} \sim Poisson(\gamma)$$`
.footnote[
**Note:** `$Loss_t = N_t - S_{t+1}$`
]

* Accounting for detection probabilities, depending on meteorological covariates:

`$$N^*{_t} \sim Bin(N_t, p)$$`

`$\Rightarrow$` **Sky condition, wind condition, temperature** & **time of the day**
]

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# Model - Dail & Madsen

* 1 MCMC chain (= 1 core) with 100 000 iterations `$\sim$` **2 days**

* 3 chains per species `$\times$` 564 species `$\Rightarrow$` **1692 MCMC chains**

.center[
`$\Rightarrow$` **9.3 years** to fit the model using 1 core ( `$\sim$` 1 year using 8 cores)
]

<br>

]

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# Change in abundance, recruitment and loss

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# Change in abundance, recruitment and loss
  
.center[
<img src="data:image/png;base64,#images/map_rec.jpg" width="100%" />
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# Change in abundance, recruitment and loss
  
.center[
<img src="data:image/png;base64,#images/map_loss.jpg" width="100%" />
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# Change in abundance, recruitment and loss
  
.center[
<img src="data:image/png;base64,#images/map_all_number.jpg" width="90%" />
]

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss

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# Recruitment vs. Loss: BBS routes

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# Recruitment vs. Loss in space

<img src="data:image/png;base64,#images/map_recVsLoss.png" width="90%" />
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# Recruitment vs. Loss in space (smoothened)

<img src="data:image/png;base64,#images/map_recVsLoss_gam.png" width="90%" />
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# Change in growth, recruitment and loss rates

<img src="data:image/png;base64,#images/map_gr.png" width="100%" />
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# Change in growth, recruitment and loss rates

<img src="data:image/png;base64,#images/map_recRate.png" width="90%" />
]

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# Change in growth, recruitment and loss rates

<img src="data:image/png;base64,#images/map_lossRate.png" width="90%" />
]

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# Change in growth, recruitment and loss rates

<img src="data:image/png;base64,#images/map_rates_all.png" width="90%" />
]

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